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Impacts of Air–Sea Interaction on Tropical Cyclone Track and Intensity
LIGUANG WU
Goddard Earth and Technology Center, University of Maryland, Baltimore County, Baltimore, and Laboratory for Atmospheres,
NASA Goddard Space Flight Center, Greenbelt, Maryland
BIN WANG
Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii
SCOTT A. BRAUN
Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland
(Manuscript received 15 July 2004, in final form 19 April 2005)
ABSTRACT
While the previous studies of the impacts of air–sea interaction on tropical cyclones (TCs) generally agree
on significant reduction in intensity and little change in track, they did not further explore the relative roles
of the weak symmetric and strong asymmetric sea surface temperature (SST) anomalies relative to the TC
center. These issues are investigated numerically with a coupled hurricane–ocean model in this study.
Despite the relatively small magnitude compared to the asymmetric component of the resulting cooling,
the symmetric cooling plays a decisive role in weakening TC intensity. A likely reason is that the symmetric
cooling directly reduces the TC intensity, while the asymmetric cooling affects the intensity through the
resulting TC asymmetries, which are mainly confined to the lower boundary and much weaker than those
resulting from large-scale environmental influences.
The differences in TC tracks between the coupled and fixed SST experiments are generally small because
of the competing processes associated with the changes in TC asymmetries and the beta drift induced by
air–sea interaction. The symmetric component of the SST drop weakens the TC intensity and outer
strength, leading to a more northward beta drift. On the other hand, since the asymmetric component of the
SST cooling is negative in the rear and positive in the front of a TC in the coupled experiments, the
enhanced diabatic heating is on the southern side of a westward-moving TC, tending to shift the TC
southward. In the coupled model the westward TCs with relatively weak (strong) outer strength tend to turn
to the north (south) of the corresponding TCs without air–sea interaction.
1. Introduction
A tropical cyclone (TC) develops and is maintained
by drawing energy from the underlying ocean surface.
It can form only over waters of 26°C or higher and its
intensity is very sensitive to the sea surface temperature
(SST; e.g., Tuleya and Kurihara 1982; Emanuel 1986).
Treating a tropical storm as a Carnot heat engine,
Emanuel (1986) suggested that the TC maximum po-
Corresponding author address: Dr. Liguang Wu, NASA GSFC,
Code 912, Greenbelt, MD 20771.
E-mail: [email protected]
© 2005 American Meteorological Society
MWR3030
tential intensity is primarily determined by the underlying SST. At the same time, the surface wind stress
associated with a TC can generate strong turbulent mixing that deepens the ocean mixed layer (OML) by entraining cooler water into the surface layer, leading to
significant SST decreases. Observations indicate that
the SST cooling caused by TCs ranges from 1° to 6°C
(Price 1981).
The feedback of the resulting cooling on TC intensity
has been investigated using coupled hurricane–ocean
models. Early experiments were performed with upper
OML models forced by axisymmetric TC models (Elsberry et al. 1976; Chang and Anthes 1979; Sutyrin and
Khain 1979). Because of the markedly rightward bias of
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the ocean response with respect to the TC track, threedimensional coupled models were used recently
(Bender et al. 1993; Falkovich et al. 1995; Chan et al.
2001; Bender and Ginis 2000). These simulations indicated that the storm-induced cooling of the OML can
significantly weaken a storm. However, given the fact
that the resulting SST anomalies comprise the axially
symmetric and asymmetric components relative to the
TC center, the relative contribution of each component
to TC motion and track has not addressed. Emanuel’s
(1999) study suggests that the symmetric component of
the storm-induced SST anomaly field may play a decisive role in reducing the storm intensity because he was
able to successfully simulate most aspects of the evolution of storm intensity using a two-dimensional (axially
symmetric) hurricane model coupled with a onedimensional ocean model oriented along the storm
track. Whether the symmetric SST anomalies can be
fully responsible for the reduction of storm intensity
will be examined here.
While the previous studies generally agree regarding
the reduction in TC intensity, they disagree concerning
the impacts of air–sea interaction on TC motion. Khain
and Ginis (1991) found that westward-moving (eastward moving) TCs in coupled experiments were displaced to the south (north) relative to the corresponding experiments without air–sea interaction. They attributed these track differences to asymmetric
precipitation patterns that were shifted azimuthally because of air–sea interaction. On the other hand, the
Bender et al. (1993) experiments with the National
Oceanic and Atmospheric Administration (NOAA)
Geophysical Fluid Dynamics Laboratory (GFDL) TC
model coupled with an eight-layer ocean model found
that the westward tracks gradually turned more to the
north relative to the track in the fixed SST experiments,
especially for slow-moving storms. Bender et al. (1993)
suggested that this track deviation is related to a systematic decrease in the azimuthally averaged tangential
flow of the TC vortex. In general, the influence of air–
sea on TC tracks is small but persistent. This study will
make an effort to understand what causes these contradictory results.
This study particularly focuses on the different ways
the symmetric and asymmetric components of the
storm-induced SST anomaly affect TC intensity and
motion. Although high-resolution models with more
sophisticated model physics can simulate the very details of real hurricanes, a coupled hurricane–ocean
model that can capture the primarily features of hurricane–ocean interaction but with intermediate complexity will be used in the present study.
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2. The coupled hurricane–ocean model and
experimental design
a. Hurricane model
The hurricane model designed by Wang (1998) consists of 201 ⫻ 201 grid points with a uniform spacing of
25 km in the horizontal and 16 vertical layers with relatively high resolution near the lower and upper boundaries. The details of the model and its capability to
simulate the motion and evolution of baroclinic TCs in
the presence of diabatic heating has been documented
by Wu (1999) and Wu and Wang (2000). The primary
model physics include large-scale condensation calculated explicitly with the method used by Leslie et al.
(1985), subgrid-scale cumulus convection parameterized with Kuo’s (1974) scheme, a Newtonian cooling as
used in the TC model by Rotunno and Emanuel (1987),
and surface fluxes of momentum, sensible and latent
heat calculated by the bulk aerodynamic method, in
which the exchange coefficients are determined following Kondo (1975) and Louis (1979).
b. Ocean model
The ocean response to the forcing of a moving hurricane may be conveniently divided into the forced and
relaxation stages (Gill 1984). The forced stage response
which typically lasts half a day or a storm residence
time, is a primarily local response and includes OML
currents of 1 m s⫺1 and substantial cooling of the OML
primarily in the right rear quadrant by the vertical mixing (Price 1981; Sanford et al. 1987; Black 1983; Shay et
al. 1992). The relaxation stage response following a hurricane passage is an inherently nonlocal baroclinic response to the wind stress curl and typically lasts 5–10
days. The energy is spread through internal waves
(Geisler 1970; Gill 1984) that penetrate into the thermocline (Shay and Elsberry 1987; Brink 1989), and
leaves behind a baroclinic geostrophic current along the
storm track. To simulate these ocean responses, the
ocean model should include OML physics and thermocline and upper ocean dynamics.
A two-and-a-half layer ocean model developed by
Wang et al. (1995) is used in this study. Since the response is primarily baroclinic, the ocean upper boundary is a rigid lid so that the barotropic response is removed. The model includes two active upper layers: an
OML and a middle thermocline layer. Below the thermocline layer is a motionless deep layer (z ⬍ ⫺h) in
which the temperature (Tr) is assumed to be constant.
In the OML (0 ⬎ z ⬎ ⫺h1), the temperature (T1) and
velocity are independent of depth, and in the thermocline layer (⫺h1 ⬎ z ⬎ ⫺h), the temperature decreases linearly from T1 to Tr.
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TABLE 1. Summary of the numerical experiments.
Fixed SST
Coupled
Symmetric SST forcing
Asymmetric SST forcing
E1F
E2F
E3F
E1C
E2C
E3C
E1S
E2S
E3S
E1A
E2A
E3A
⫺1
E1: f plane, ⫺4 m s
E2: ␤ plane, 0 m s⫺1
E3: ␤ plane, ⫺4 m s⫺1
Since the ocean model was originally developed for
study of ocean phenomena on the interannual time
scale, a number of aspects of the model physics are
modified to better simulate the ocean response to the
forcing of a moving hurricane. First, following Bender
et al. (1993), the Kraus–Turner scheme (Kraus and
Turner 1967) to parameterize the vertical turbulent
mixing (entrainment) is replaced by the Deardorff’s
scheme (Deardorff 1983) to include the important
shear instability (Ginis 1995). According to Deardorff
(1983), a singularity occurs in the Kraus–Turner
scheme when the velocity shear is significant. Second,
in the modified model it is assumed that the downward
heat flux decreases exponentially in the mixed layer
and the turbulent momentum and heat fluxes are not
allowed to penetrate below the OML base. The TC–
ocean interaction is through the surface turbulent
fluxes of momentum, sensible and latent heat. The energetics of the OML has been studied extensively for
the last two decades. Although no consensus exists so
far on the amount of turbulent energy radiated from
the mixed layer, some theoretical and laboratory analyses suggest that the bulk of the energy fed into the
mixed layer is trapped by the transition layer and is
eventually dissipated by wave breaking (Fernando
1991). This scenario is probably appropriate for the
ocean areas that experience the most intense TCs (Ginis 1995). Third, parameterizations of the temperature
of entrained water are a key to closure of the OML
equations (Wang et al. 1995). The original model considers a thin entrainment layer existing just below the
OML base. This entrainment layer is a thin region of
vigorous small-scale mixing, within which the turbulent
flux drops sharply from a finite value to zero. The vertical temperature gradient in the entrainment layer with
thickness ⌬he is assumed to be proportional to the
mean vertical temperature gradient in the thermocline
layer, that is,
T1 ⫺ Te ⫽ k⌬he
T1 ⫺ Tr
,
h ⫺ h1
共1兲
where Te is the temperature of the entrainment layer
and k ⫽ 1 was used in the original model. In the response of ocean to the TC forcing shown by Shay et al.
(1992), the temperature gradient between the OML
and the top of the thermocline can be much larger than
the mean vertical temperature gradient in the thermocline. Based on the results of Shay et al. (1992), we
assume k ⫽ 3.
The ocean is initially assumed to be horizontally homogeneous and quiescent. The water temperature in
the deep resting layer is set to 10°C. The entrainment
layer depth is 5 m, which is identical to that used by
Wang et al. (1995). The initial OML depth and temperature are also two important parameters. Sensitivity
tests show that the magnitude of the cooling in this
layer increases with decreasing initial depth or increasing initial SST. Moreover, the magnitude of the OML
cooling also increases with increasing depth or temperature gradient associated with the thin entrainment
layer. However, the cooling patterns are generally similar. For this reason, the depth of the mixed layer is
initially set to 35 m in all coupled experiments. The
ocean model has the same grid spacing and domain size
as the hurricane model. The SST and wind stress are
passed between the hurricane and ocean models every
3 min. Periodic lateral boundary conditions are used in
the hurricane and ocean models.
c. Experimental design
Three sets of idealized numerical experiments are
conducted with different environmental influences
(Table 1). The ocean response depends on whether the
TC speed exceeds the long gravity wave speed or not.
In the current ocean model, the phase velocity of long
gravity waves is about 1.2 m s⫺1 for the first baroclinic
mode. The simulation of the cold wake behind a storm
requires that the translation speed of the TC is greater
than the gravity wave speed. The first set of numerical
experiments (E1) are designed to be the simplest case,
which are run on an f plane with a horizontally uniform
easterly ambient flow ⫺4 m s⫺1. The second set of numerical experiments (E2) are on a beta plane in a resting environment, in which the vortex movement arises
from the beta drift. The third set of numerical experiments (E3) are a combination of E1 and E2, that is,
they include the influences of uniform easterly flow and
the beta effect.
For each set, four experiments are conducted: fixed
SST, coupled, symmetric-only SST forcing, and asym-
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metric-only SST forcing (Table 1). For example, E1F,
E1C, E1S, and E1A, respectively, are referred to these
four experiments in set E1. In the fixed SST experiments, the air–sea coupling is excluded and the SSTs
are fixed in time and horizontally uniform (29.5°C for
E1 and 28.5°C for E2 and E3). The coupled experiments are run with full air–sea coupling. The SST
anomalies in the coupled experiments are saved each
hour and decomposed into their symmetric and asymmetric components with respect to the TC center. The
symmetric SST component can directly affect the intensity of the TC’s symmetric circulation while the asymmetric component affects the TC through the interaction between the mean TC circulation and the induced
asymmetric circulation. Because the different ways the
two components influence TC intensity and track are
different, two more uncoupled experiments are run using the sum of the horizontal uniform SST and the timedependent symmetric or asymmetric SST anomalies derived from the corresponding coupled experiments as
the SST forcing, respectively. For convenience, these
experiments are called symmetric-only and asymmetric-only SST forcing experiments in this paper.
All experiments begin with an identical, initially symmetric baroclinic vortex. The intensity of the initial vortex decreases with height, but without an anticyclonic
circulation atop. The maximum tangential wind (␷m) of
25 m s⫺1 at rm ⫽ 100 km is at the lowest model level.
The horizontal wind profile [␷(r)] is generated following
␷共r兲 ⫽ ␷m
冉 冊
冋 冉 冊册
1
r
r
exp
1⫺
rm
b
rm
b
,
共2兲
where r and b are the radius from the TC center and the
shape parameter, respectively. Here, b is set to 0.5 in
sets E1, E2, and E3. The change in this parameter primarily affects the outer strength of the initial vortex,
which affects the magnitude of the beta drift. To examine the influence of air–sea interaction on the beta drift,
three additional experiments conducted are the same as
E2 except that the shape parameter is 0.3 for B1, 1.0 for
B2, and 1.2 for B3.
3. Ocean response in the coupled model
In this section we focus on the coupled experiment in
set E2 (E2C) since the general patterns of the ocean
response to TC forcing are in general similar for all the
experiments. The time series of the maximum current
speeds in the OML and thermocline layer and the minimum OML temperature are shown in Figs. 1a,b. The
OML current increases quickly while the minimum
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FIG. 1. Time series of the maximum ocean responses: (a) currents (cm s⫺1) in the mixed (solid) and thermocline (dashed) layers, and (b) sea surface temperature.
temperature decreases rapidly during the first 24 h, and
both reach a quasi–steady state after 24 h. However, the
thermocline current continues to accelerate until 72 h.
The maximum mixed layer cooling of 3.5°C at 33 h is
generally consistent with ocean observations since the
storm translation due to the beta drift is only 2–4 m s⫺1.
Black (1983) found that storms moving faster (slower)
than 3 m s⫺1 can produce 1°–3°C (3°–5°C) cooling.
When the SST reaches its minimum value, the OML
current is about 1.1 m s⫺1. Thereafter, the current increases slowly and attains its maximum of 1.2 m s⫺1 at
56 h. The magnitude of the resulting OML currents also
compares favorably with observations (e.g., Shay et al.
1992) and numerical simulations with other sophisticated coupled models (e.g., Bender et al. 1993).
The ocean responses at 96 h in E2C have negative
SST anomalies over a large area with a cold wake along
the TC track (Fig. 2a). The cooling has a pronounced
rightward bias with respect to the TC track and the
maximum cooling is immediately behind the TC center.
The pattern of the OML cooling is consistent with the
rightward-biased OML deepening (Fig. 2b). The largest
entrainment rate, which is parameterized as a function
of wind stress, velocity shear at the base of the mixed
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FIG. 2. Ocean response by 96 h in the coupled experiment E2C: (a) sea surface temperature anomaly (°C); (b) mixed layer depth
anomaly (m, positive values indicate greater depths); (c) entrainment rate (cm s⫺1); (d) thermocline depth anomaly (m, negative values
indicate shallowing depths); (e) currents in the mixed layer (cm s⫺1), and (f) currents in the thermocline layer (cm s⫺1). The TC track
starts from the rhs and the center positions every 12 h are indicated with closed circles.
layer, and convective overturning due to the surface
buoyancy fluxes, is primarily confined to the vicinity of
the TC center (Fig. 2c). However, the ocean inertiagravity waves excited by moving TCs also contribute
some OML deepening in the wake of the TC (Gill
1984).
The region of the maximum OML deepening occurs
well behind the TC center on the right side of the TC
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track. The maximum deepening reaches 63 m at 44 h
and decreases to about 45 m at 96 h. This is also comparable with the observational analysis of Hurricane
Gilbert (1988) by Shay et al. (1992). They found that
storm passage increased the OML depth from prestorm
values of 30–35 m to approximately 60 m on the righthand side of the track. The pattern of OML deepening
is also similar to that simulated with the GFDL coupled
model for Hurricane Norbert (Bender et al. 1993). The
model OML currents are presented in Fig. 2e. In the
front of the TC, the cyclonically rotating wind stress
generates OML currents with significant divergence
and the current pattern becomes significantly asymmetric behind the TC. The thermocline depth has negative
anomalies behind the TC center without significant biases with respect to the track (Fig. 2d). The slightly
positive anomalies outside the negative anomalies are
an indication of the horizontal dispersion of inertiagravity waves after the TC passing. Compared to the
OML currents, the thermocline currents, which are primarily driven by the depth gradient (Bender et al.
1993), are relatively small (Fig. 2f).
In summary, the major features of the simulated
ocean response in the current coupled hurricane–ocean
model, that is, the amplitudes and spatial patterns of
the OML cooling and deepening, the thermocline
depth anomalies, and the induced ocean currents in the
mixed and thermocline layers, are all in good agreement with observations and previous numerical simulations. Therefore, the current ocean model is capable
of realistically simulating the response of the ocean to
slowly moving TCs as in this experiment.
4. Influence of air–sea interaction on TCs
a. Intensity change
The TC intensities for sets E1, E2, and E3 are compared with the corresponding fixed-SST experiments in
terms of the maximum wind speed and the minimum
central pressure (Fig. 3). In agreement with previous
numerical studies (e.g., Chang and Anthes 1979; Khain
and Ginis 1991; Bender et al. 1993; Bender and Ginis
2000), the present simulations confirm that air–sea interaction reduces TC intensity as a result of mixed layer
cooling. In set E1, the TC reaches a maximum wind of
60.1 m s⫺1 and a central pressure of 917 mb without the
inclusion of air–sea interaction (E1F). When the air–
sea coupling is included (E1C), the maximum wind is
reduced by about 12 m s⫺1 and the central surface pressure decreases by 32 mb. In set E2, the coupling leads to
differences of 14 m s⫺1 in the maximum wind and 24 mb
in the minimum central pressure. When the beta effect
and environmental flow are combined (E3), the air–sea
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interaction reduces the maximum wind by 10 m s⫺1 and
increases the central pressure by 18 mb.
The decomposition of the SST anomaly field shown
in Fig. 2a shows that the symmetric SST component
extends over a large area with an average magnitude of
1.5°C in the inner core region (Fig. 4a) and that the
asymmetric SST pattern has a cold wake of negative
anomalies behind the center and positive anomalies in
front of the center (Fig. 4b). As shown in Fig. 3, the TC
intensities in the symmetric-only and asymmetric-only
SST forcing experiments are nearly identical to those in
the coupled and fixed-SST experiments, respectively,
except for small fluctuations. This result suggests that
the intensity reduction in the coupled experiments is
primarily caused by the symmetric component of the
induced SST drop, while the asymmetric component of
the SST anomalies resulting from air–sea coupling only
plays a minor role in the intensity change.
In principle, the asymmetric SST field can affect TC
intensity only through the resulting inner-core TC
asymmetries. To examine the asymmetries associated
with the asymmetric SST forcing, the asymmetric winds
in the fixed-SST experiments are compared to those in
the asymmetric-only SST forcing experiments. The differences of the asymmetric winds between these two
experiments are considered to be the primary result of
the asymmetric SST forcing. Compared to the asymmetric winds resulting from the beta effect (Fig. 5a), the
winds induced by the asymmetric SST forcing (Fig. 5b)
are mainly confined to a small region associated with
the significant SST anomalies, with the largest differences over the warm anomaly. Moreover, the resulting
asymmetric winds are confined primarily to the lower
model levels (figure not shown). Therefore the asymmetries induced by the asymmetric SST forcing play an
insignificant role in TC intensity change.
b. The TC tracks
The TC tracks between the coupled and fixed SST
experiments are shown in Fig. 6. The influence of air–
sea coupling on TC tracks is relatively small but persistent. In agreement with those of the westward-moving
TCs simulated by Khain and Ginis (1991), the TCs in
the coupled experiments are displaced to the south
relative to the corresponding experiments without air–
sea interaction for sets E1, E2, and E3. By 96 h, the
track differences for sets E1, E2, and E3 are 100, 29,
and 40 km, respectively.
The asymmetric convection with respect to a TC center can directly affect TC motion. Wu and Wang (2001)
suggested that wavenumber-1 diabatic heating with respect to the TC center can generate a positive potential
vorticity tendency and thus can shift the TC to the
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FIG. 3. Time series of the maximum wind speed (m s⫺1, left) and minimum central pressure (mb, right) in experiments E1 (a), (b);
E2 (c), (d); and E3 (e), (f). The open and solid circles denote the fixed and asymmetric-only SST forcing experiments while the open
and solid squares indicate the coupled and symmetric-only SST forcing experiments.
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FIG. 4. Decomposition of the SST anomalies at 96 h resulting
from hurricane–ocean interaction in the coupled experiment of
set E2 (E2C): (a) the symmetric SST component and (b) the
asymmetric SST component (°C). Contour intervals are 0.5°C.
maximum heating region. Willoughby (1992) investigated asymmetric convective forcing in a tropical cyclone as a mass source-sink pair. When the mass source
sink maintains the same orientation with respect to the
center, quasi-stationary gyres are established and persistently advect the vortex center toward the enhanced
convection. In an example, the TC was shifted by 20 km
in 18 h (0.3 m s⫺1). Since the diabatic heating is dominated by the latent heat release, the asymmetry of diabatic heating can be displayed with the total rainfall
rates. Figure 7 shows the time evolution of the rainfall
rates for the fixed SST (E1F), the asymmetric-only SST
forcing (E1A), and the symmetric-only SST forcing
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(E1S) experiments in set E1. The mechanisms responsible for the generation of the rainfall asymmetry have
been discussed in previous studies (Shapiro 1983; Peng
et al. 1999; Wu and Braun 2004).
The rainfall asymmetries are changed in response to
the time-dependent symmetric and asymmetric SST
forcings. After 24 h, the rainfall rate in the experiment
with asymmetric-only SST forcing (Fig. 7b) increases
compared with the fixed SST experiment (Fig. 7a). A
possible reason is that the slightly positive SST anomalies ahead of the TC center enhance the surface fluxes
and thus the rainfall. Second, the higher SST than that
in the coupled and symmetric-only SST forcing experiments leads to a more intense TC circulation in the
asymmetric-only SST forcing and fixed-SST experiments. Because the stronger storms axisymmetrize the
asymmetries more effectively than the weaker storms,
the asymmetries appear less in the fixed-SST and asymmetric forcing experiments. This is consistent with the
fact that intense hurricanes tend to be rather symmetric
(Willoughby et al. 1984).
Although the TCs are primarily steered by the easterly environmental flow, the track differences shown in
Fig. 8 are consistent with the asymmetries of the rainfall
pattern. Note that the ordinate scale is much smaller
than the abscissa in Fig. 8. In the symmetric-only SST
forcing experiment (Fig. 7c), the strongest rainfall is
always on the northern side after 24 h, and the TC
persistently moves northwestward. In the fixed SST experiment (Fig. 7a), the TC persistently moves northwestward by 72 h. The shift of the rainfall asymmetry
from the northwest to the west since 60 h causes the TC
to move westward. In the asymmetric-only SST forcing
experiment (Fig. 7b), the region with enhanced rainfall
shifts to the southwestern side, leading to a southward
shift in the TC track after 48 h.
For the fixed SST experiment in sets E2 and E3, the
TCs move northwestward (Figs. 6b,c). As time progresses, the beta gyres develop and intensify, gradually
leading to a shift in the precipitation pattern. In addition to the mechanism discussed for E1, the beta gyres
and their associated southeasterly vertical shear can
also affect the asymmetries of the precipitation pattern
(Peng et al. 1999; Frank and Ritchie 1999, 2001). The
rainfall in E2F at 24 h intensifies primarily ahead of the
TC center (Fig. 9a). At 48 and 72 h, the shift of the
primary rainfall rate maximum to the eastern side results from the impacts of the beta gyres. For the fixedSST experiment of set E3 (Fig. 10a), the rainfall pattern
is similar to that E1F shown in Fig. 7a, which suggests
the dominant influence of the environmental flow. In
the presence of air–sea coupling (Figs. 9b and 10b), the
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FIG. 5. (a) The lowest-level (about 990 mb) asymmetric wind field in the fixed SST
experiment of set E2 (E2F) and (b) the wind difference between the asymmetric-only
SST forcing (E2A) and fixed SST (E2F) experiments at 96 h. The asymmetric component of the SST anomalies is superposed at an interval of 0.5°C. The TC is located at
the domain center.
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FIG. 6. The TC tracks in the fixed SST (dashed) and coupled (solid) experiments for sets (a) E1, (b) E2, (c) E3, (d) B2, (e) B1, and
(f) B3. The TCs generally move westward and the center locations every 12 h are indicated with circles.
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FIG. 7. Evolution of rainfall rates (mm h⫺1) in (a) the fixed SST, (b) asymmetric-only SST forcing, and (c) symmetric-only SST
forcing experiments of set E1. The contour intervals are 5 mm h⫺1.
rainfall patterns exhibit more prominent wavenumber-1 asymmetries. With the maxima of the rainfall
rates generally occurring in the southern region of the
westward-propagating TCs after 24 h, we hypothesize
that the favorable location is associated with the asymmetric SST anomalies resulting from air–sea coupling.
If we consider the cyclonic rotation of air parcels as
they rise, the enhanced (suppressed) rainfall rates are
related to the positive (negative) SST anomalies ahead
of (behind) the TC center. These persistent rainfall
asymmetries tend to shift the TC tracks slightly southward in the coupled experiments of sets E2 and E3
(Figs. 7b,c).
Bender et al. (1993) suggested that in experiments
with air–sea interaction, a systematic weakening of the
mean tangential flow at all radii alters the orientation of
the beta gyres and thus affects the beta drift. The resulting secondary steering flow associated with the beta
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FIG. 8. The TC tracks in the fixed (solid circles), symmetric-only (open squares), and
asymmetric-only (open circles) SST experiments for set E1. The TCs generally move
westward and the center positions are indicated every 12 h.
gyres in the coupled experiments rotates anticyclonically relative to that in the fixed-SST experiments
(Fiorino and Elsberry 1989; Wang et al. 1997). As a
result, the westward tracks gradually turn more to the
north relative to the track in the fixed SST experiments.
The influence of the beta drift and its association with
the outer vortex strength can be investigated by adjusting the shape parameter (b) of the initial vortex profile.
In E1, E2, and E3, b ⫽ 0.5. When b is made smaller
(larger) than 0.5, the outer portion of the vortex is
strengthened (weakened). Since the resulting SST cooling is primarily a function of TC intensity and translation, the weakening of the TC circulation is nearly independent of the outer vortex strength or the shape
parameter. In this case, the relative decrease in the
outer vortex strength is larger for a vortex with initially
weak strength than for one with initially strong strength
(Fig. 11). Thus the change in the northward beta drift is
larger for the former than for the latter. While the influence of the asymmetric diabatic heating remains the
same, in agreement with Khain and Ginis (1991) the
vortex track in the coupled model shifts more southward when the outer part of the vortex is stronger (b ⫽
0.3; Fig. 6e), and in agreement with Bender et al. (1993)
the vortex in the coupled model shifts more northward
when the vortex strength is weaker (b ⫽ 1.0 and 1.2;
Figs. 6d,f).
Therefore the influence of air–sea interaction on TC
tracks is a result of the competing effects of the asym-
metries associated with the resulting SST anomalies
and changes in the beta drift associated with the outer
wind weakened by the air–sea coupling. For this reason,
the net track differences between the coupled and
fixed-SST experiments are generally small.
5. Conclusions and discussion
The impacts of air–sea interaction on TC intensity
and track are investigated using a coupled hurricane–
ocean model. Three sets of numerical experiments are
designed with idealized environmental influences. For
each set, four experiments are conducted with fixed
SST, air–sea coupling, symmetric-only SST forcing, and
asymmetric-only SST forcing, respectively. In the latter
two experiments, the time-dependent SST forcing is deduced from the hourly output of the corresponding
coupled experiments. The coupled model, which consists of a hydrostatic hurricane model and an intermediate ocean model with an OML and a middle thermocline layer. Compared with observations and previous numerical simulations, can reasonably produce the
major features of the ocean responses to moving TC
forcing, including OML deepening, SST cooling, and
OML and thermocline layer currents.
Although the negative SST anomalies associated
with the asymmetric component are generally larger in
magnitude than those associated with the symmetric
component, the influence of the asymmetric compo-
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WU ET AL.
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FIG. 9. Evolution of rainfall rates (mm h⫺1) in the (a) fixed SST and (b) coupled
experiments of set E2.
nent is insignificant while the resulting symmetric cooling plays a decisive role in weakening TCs in the
coupled experiments. The asymmetric SST forcing affects TC intensity only through the resulting asymmetries in the TC circulation, but the asymmetric winds
induced by the asymmetric SST forcing are mainly confined to the lower boundary and are much weaker than
the asymmetric winds induced by large-scale environmental influences such as uniform flows and the beta
effect. This result concurs with Emanuel’s (1999) finding that the evolution of storm intensity can be success-
fully simulated by including only the symmetric SST
decreases caused by air–sea coupling.
The asymmetric SST forcing intensifies the rainfall
rates on the front left-hand side (relative to TC motion). The symmetric SST forcing weakens the TC circulation and thus the axisymmetrization process, thus
reinforcing convective asymmetry, meanwhile, the
weakening of the outer portion of the mean vortex alters the orientation of the beta gyres and leads to more
northward beta drift. For the experiments including the
beta effect (E2 and E3), the enhanced TC heating
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FIG. 10. Same as Fig. 9 but for E3.
asymmetries tend to shift westward-moving TCs southward while the modified beta drift tends to shift TCs
northward in the coupled experiments. Because of the
opposing effects, the resulting track difference between
the fixed-SST and coupled experiments is generally
small. The different effects of air–sea interaction on TC
tracks simulated by Khain and Ginis (1991) and Bender
et al. (1993) can be reconciled by adjusting the vortex
outer strength. When the outer vortex strength is relatively weak (strong), a TC in the coupled model moves
to the north (south) of the TC in the corresponding
fixed SST experiments.
We should mention that this study particularly focuses on the different ways the symmetric and asymmetric components of the SST anomalies induced by
air–sea interaction affect TC intensity and track. Compared with the complicated hurricane–ocean coupling
in real cases, the complexity of the coupled model used
in this study has been largely simplified. Although the
model can simulate the most important features we
know so far, some caveats shall be kept in mind as we
interpret these results. First, due to the relatively coarse
horizontal model resolution, there is no explicit convection schemes for the complex moist processes that are
NOVEMBER 2005
WU ET AL.
FIG. 11. Relative decreases of the 850-mb symmetric tangential
wind at 72 h due to air–sea interaction for cases b ⫽ 0.5 (E2C,
solid) and b ⫽ 1.0 (B2, dashed).
very important for TCs. Second, the boundary layer is
parameterized with the simple bulk scheme, and some
important processes in the inflow boundary layer such
as sea spray are not included in this coupled model
(Barnes et al. 2004). These caveats may make the extents and magnitudes of the simulated ocean cooling
and the atmospheric response such as precipitation less
realistic. However, we believe that the simplification in
the model physics may not qualitatively affect the results presented in this paper.
Acknowledgments. The authors thank three anonymous reviewers for their thorough editorial efforts and
insightful comments on an earlier version of the paper,
which lead to much improvement in the presentation of
this study. Liguang Wu and Scott Braun thank Dr. R.
Kadar (NASA HQ) for his support through the NASA
CAMEX program. Bin Wang acknowledges the support by Office of Naval Research under Award
N00014-021-0532.
REFERENCES
Barnes, G., R. Schneider, and S. Houston, 2004: Vertical profiles
of thermodynamic variables in Hurricanes Bonnie (1998) and
Mitch (1998): Implications for energy transport into the inflow layer. Preprints, 26th Conf. on Hurricanes and Tropical
Meteorology, Miami, FL, Amer. Meteor. Soc., 653–654.
Bender, M. A., and I. Ginis, 2000: Real-case simulations of hurricane–ocean interaction using a high resolution coupled
model: Effects on hurricane intensity. Mon. Wea. Rev., 128,
917–946.
——, ——, and Y. Kurihara, 1993: Numerical simulations of hurricane–ocean interaction with a high resolution coupled
model. J. Geophys. Res., 98, 23 245–23 263.
Black, P. G., 1983: Ocean temperature changes induced by tropical cyclones. Ph.D. dissertation, Pennsylvania State University, 278 pp.
Brink, K. H., 1989: Observations of the response of the ther-
3313
mocline currents to a hurricane. J. Phys. Oceanogr., 19, 1017–
1022.
Chan, J. C.-L., Y. Duan, and L. K. Shay, 2001: Tropical cyclone
intensity changes from a simple ocean–atmosphere coupled
model. J. Atmos. Sci., 58, 154–172.
Chang, S. W., and R. A. Anthes, 1979: The mutual response of the
tropical cyclone and the ocean. J. Phys. Oceanogr., 9, 128–
135.
Deardorff, J. W., 1983: A multi-limit layer entrainment formulation. J. Phys. Oceanogr., 13, 988–1002.
Elsberry, R. L., T. S. Fraim, and R. N. Trapnell Jr., 1976: Mixed
layer model of the oceanic thermal response to hurricanes. J.
Geophys. Res., 81, 1153–1163.
Emanuel, K. A., 1986: An air–sea interaction theory for tropical
cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43,
585–604.
——, 1999: Thermodynamic control of hurricane intensity. Nature, 401, 665–669.
Falkovich, A. I., A. P. Khain, and I. Ginis, 1995: Motion and evolution of binary tropical cyclones in a coupled atmosphere–
ocean numerical model. Mon. Wea. Rev., 123, 1345–1363.
Fernando, H. J., 1991: Turbulent mixing in stratified fluids. Annu.
Rev. Fluid Mech., 23, 455–493.
Fiorino, M. J., and R. L. Elsberry, 1989: Some aspects of vortex
structure related to tropical cyclone motion. J. Atmos. Sci.,
46, 975–990.
Frank, W. M., and E. A. Ritchie, 1999: Effects on environmental
flow upon tropical cyclone structure. Mon. Wea. Rev., 127,
2044–2061.
——, and ——, 2001: Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes. Mon.
Wea. Rev., 129, 2249–2269.
Geisler, J. E., 1970: Linear theory of the response of a two layer
ocean to a moving hurricane. Geophys. Fluid Dyn., 1, 249–
272.
Gill, A. E., 1984: On the behavior of inertial waves in the wakes of
storm. J. Phys. Oceanogr., 14, 1129–1151.
Ginis, I., 1995: Ocean response to tropical cyclones. Global perspectives on tropical cyclones. WMO/TD 693, 218–256.
Khain, A. P., and I. Ginis, 1991: The mutual response of a moving
tropical cyclone and the ocean. Beitr. Phys. Atmos., 64, 125–
141.
Kondo, J., 1975: Air–sea bulk transfer coefficients in diabatic conditions. Bound.-Layer Meteor., 9, 91–112.
Kraus, E. B., and J. S. Turner, 1967: A one-dimensional model of
the seasonal thermocline. Part II: The general theory and its
consequences. Tellus, 19, 98–105.
Kuo, H. L., 1974: Further studies of the parameterization of the
influence of cumulus convection on large-scale flow. J. Atmos. Sci., 31, 1232–1240.
Leslie, L. M., G. A. Mills, L. W. Logan, D. J. Gauntlett, G. A.
Kelly, M. J. Manton, J. L. McGregor, and J. M. Sardie, 1985:
A high resolution primitive equations NWP model for operations and research. Aust. Meteor. Mag., 33, 11–35.
Louis, J. F., 1979: A parametric model of vertical eddy fluxes in
the atmosphere. Bound.-Layer Meteor., 17, 746–756.
Peng, M. S., B.-F. Jeng, and R. T. Williams, 1999: A numerical
study on tropical cyclone intensification. Part I: Beta effect
and mean flow effect. J. Atmos. Sci., 56, 1404–1423.
Price, J. F., 1981: Upper ocean response to a hurricane. J. Phys.
Oceanogr., 11, 153–175.
Rotunno, R., and K. A. Emanuel, 1987: An air–sea interaction
theory for tropical cyclones. Part II: Evolutionary study using
3314
MONTHLY WEATHER REVIEW
a nonhydrostatic axisymmetric numerical model. J. Atmos.
Sci., 44, 542–561.
Sanford, T. B., P. G. Black, J. R. Haustein, J. W. Feeney, G. Z.
Forristall, and J. F. Price, 1987: Ocean response to a hurricane. Part I: Observations. J. Phys. Oceanogr., 17, 2065–2083.
Shapiro, L. J., 1983: Asymmetric boundary layer flow under a
translating hurricane. J. Atmos. Sci., 40, 1984–1998.
Shay, L. K., and R. L. Elsberry, 1987: Near-inertial ocean current
response to Hurricane Frederic. J. Phys. Oceanogr., 17, 1249–
1269.
——, P. G. Black, A. J. Mariano, J. D. Hawkins, and R. L. Elsberry, 1992: Upper ocean response to Hurricane Gilbert. J.
Geophys. Res., 97, 20 227–20 248.
Sutyrin, G. G., and A. P. Khain, 1979: Interaction of the ocean
and the atmosphere in the area of moving tropical cyclones.
Dokl. Akad. Sci. USSR, 249, 467–470.
Tuleya, R. E., and Y. Kurihara, 1982: A note on the sea surface
temperature sensitivity of a numerical model of tropical
storm genesis. Mon. Wea. Rev., 110, 2063–2069.
Wang, B., T. Li, and P. Chang, 1995: An intermediate model of
the tropical Pacific Ocean. J. Phys. Oceanogr., 25, 1599–1616.
——, X. Li, and L. Wu, 1997: Hurricane beta drift direction in
horizontally sheared flows. J. Atmos. Sci., 54, 1462–1471.
VOLUME 133
Wang, Y., 1998: On the bogusing of tropical cyclones in numerical
models: The influence of vertical structure. Meteor. Atmos.
Phys., 65, 153–170.
Willoughby, H. E., 1992: Linear motion of a shallow-water barotropic vortex as an initial-value problem. J. Atmos. Sci., 49,
2015–2031.
——, F. D. Marks Jr., and R. J. Feinberg, 1984: Stationary and
moving convective bands in hurricanes. J. Atmos. Sci., 41,
3189–3211.
Wu, L., 1999: Study of tropical cyclone motion with a coupled
hurricane–ocean model. Ph.D. dissertation, University of Hawaii at Manoa, 212 pp.
——, and B. Wang, 2000: A potential vorticity tendency diagnostic approach for tropical cyclone motion. Mon. Wea. Rev.,
128, 1899–1911.
——, and ——, 2001: Effects of convective heating on movement
and vertical coupling of tropical cyclones: A numerical study.
J. Atmos. Sci., 58, 3639–3649.
——, and S. A. Braun, 2004: Effects of environmentally induced
asymmetries on hurricane intensity: A numerical study. J.
Atmos. Sci., 61, 3065–3081.